Complex Number Theory without Imaginary Number (i)

DOI: 10.4236/oalib.1100856   PDF        1,598 Downloads   2,663 Views  

Abstract

In this paper new method is introduced for complex numbers; this method does not include imaginary number “i” but produces the same results that occur in Addition, Subtraction, Multiplication & Division of complex numbers, also proof of Eluer Formula e and De Moivre theorem without using imaginary number “i”. Furthermore placing the light on the square root of a negative number, the square root of a negative number is equal to the square root of the same positive real number but with an angle of 90 degree to real line. The intention is that there’s nothing mystical about imaginary number “i”. The square root of minus one is just as real as any other number. Complex numbers exists without imaginary number “i”. This paper is limited to the results which are already established.

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Gode, D. (2014) Complex Number Theory without Imaginary Number (i). Open Access Library Journal, 1, 1-13. doi: 10.4236/oalib.1100856.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] Narayan, S. and Mittal, P.K. (2005) Theory of Functions of a Complex Variable. S. Chand & Company Ltd., New Delhi.
[2] Schneider, C. (2011) De Moivre’s Theorem—A Literature and Curriculum Project on Roots, Powers, and Complex Numbers. Department of Mathematics and Statistics, Portland State University.
[3] Bogomolny, A. (1996-2014) Cut the Knot! An Interactive Column Using Java Applets.
http://www.cut-the-knot.org/arithmetic/algebra/ComplexNumbers.shtml
[4] Cain, G. (1999-2014) Complex Analysis.
http://people.math.gatech.edu/~cain/winter99/complex.html

  
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